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Statistical Thermodynamics of Materials
MatSc 597c

Boris Veytsman[*] - Michael Kotelyanskii[*]

Fall 1997
Tue & Thur, 1:00pm-2:15pm, 325 Steidle Bldg


This is the course we taught at PennState in the Fall Semester of 1997. By popular demand we put the notes back online. We did not make any changes besides updating our addresses.

BV and MK, August 2011


This course is intended to be an introduction to Statistical Thermodynamics for students with varied skills and background. Previous experience in Thermodynamics is not required. The main objective of the course is to teach MatSci, ChemE, Chem and Phys students the language of Statistical Thermodynamics. We want to make them able to read the literature in their fields without feeling clueless and to use it for their research and learning.

This course is mainly devoted to classical (i. e. not quantum) condensed matter. We will focus on problems important for material science, polymer science and chemical engineering. In particular, this course will cover fundamentals of scattering, theory of phase equilibria, computer simulations methods (Monte Carlo & Molecular Dynamics).

The parts of the course marked ``optional'' below will be included in the lectures if the majority (or substantial minority) of students needs them for their research or learning and requests them.

Structure and Grading

This is a three credit course with two 1.5 hours lectures on Tuesdays and Thursdays. There will be no final, and the grading will be based on homeworks, classroom participation and final projects.

We will use mostly D. A. McQuarrie Statistical Mechanics and H. Ted Davis Statistical Mechanics of Phases, Interfaces and Thin Films with some asides and deviations. The notes of the course will be posted on the Web.


We will keep in mind a student that learned basic calculus and physics long time ago and forgot most of it. We require MATH140, 230, 231, PHYS 200-203 or equivalent courses. There will be several ``math refreshment'' lectures in the beginning of this course.



Math refreshment.

Closed and open systems, statistical ensembles, partition function, equivalence of ensembles, thermodynamic limit. Entropy and free energy. Boltzmann distribution. First and Second laws of thermodynamics. Fluctuations.

Optional: Polymer chain statistics & RIS model.

Gases, Liquids, Crystals

Ideal Gases. Imperfect gases and thermodynamic perturbation theory. Virial expansion. Van der Waals gases. Liquids. The law of corresponding states. Mean field approximation. Density correlation function and structure factor. Liquid state theory. Classic theory of crystalline solids.

Phase Transitions and Phase Equilibria

Thermodynamic inequalities. Stability. Phase equilibrium. Gibbs phase rule. Binodal and spinodal. Maxwell construction. Lattice theories. Ising model and lattice gas. Optional: Flory lattice theory.

Optional: Percolation and real space renormalization.


Composition fluctuations and small angle scattering. Time dependent fluctuations and Brownian motion. Langevin equation.

Optional: Kinetics of spinodal decomposition.

Computer Simulations

Monte Carlo and molecular dynamics. Sampling statistical ensembles. Detailed balance. Metropolis and smart Monte Carlo algorithms. Molecular dynamics. Numerical integration schemes. Periodic boundary conditions. Calculating kinetic and thermodynamic properties in computer simulations.


E-mail:, Home page:

E-mail:, Home page:

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© 1997 Boris Veytsman and Michael Kotelyanskii
Tue Oct 28 20:42:46 EST 1997